Hyperbolic 3-Manifolds with Boundary Which are Side-Pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-Sphere

Authors

DOI:

https://doi.org/10.37256/cm.5220242910

Keywords:

3-manifolds with boundary, link complement, knotted graph

Abstract

In this paper, we give a generalization of Ivanšić's method for hyperbolic 3-manifolds without boundary, which allows us to recognize if a hyperbolic 3-manifold with totally geodesic boundary, given by an isometric sidepairing of two hyperbolic truncated tetrahedra, is the exterior of a knotted graph; i.e., it is the complement of a 1-manifold with isolated singularities embedded in S3, in which case we get the corresponding diagram of the knotted isotopy class of its boundary. Otherwise, we obtain that the corresponding 3-manifold with boundary is the exterior of a knotted graph embedded in some lens space. Finally, we apply this method to a noncompact 3-manifold with a totally geodesic surface boundary of genus 2.

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Published

2024-04-26

How to Cite

1.
Díaz JP, Hinojosa G. Hyperbolic 3-Manifolds with Boundary Which are Side-Pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-Sphere. Contemp. Math. [Internet]. 2024 Apr. 26 [cited 2024 Oct. 13];5(2):2109-23. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2910